Overstimulation Due to Pain: Bebe and Jasper 

Sometimes cats nip/bite due to pain. They might be sensitive to touch, or they might have a more serious health problem.
Bebe and Jasper are examples of shelter cats who nip/bite when their tails are touched. We simply learned to pet them elsewhere.
Bebe and Jasper are senior cats that may have some degree of chronic pain due to arthritis. Also, because Jasper is overweight, he may experience pain due to the extra stress on his joints.
If your cat is sensitive to touch, please have them assessed by a vet. Your vet might suggest a pain management plan for arthritis or discover that your cat is suffering from an illness or disease.
As a cat behavior consultant, I've learned that behavior is rarely simple.